We study a new set of duality relations between weighted,combinatoric invariants of a graph G.The dualities arise from a non-linear transform B,acting on the weight function p.We define B on a space of real-valued functions O and investigate its properties.We show that three invariants (the weighted independence number,the weighted Lovász number,and the weighted fractional packing number) are fixed points of B2,but the weighted Shannon capacity is not.We interpret these invariants in the study of quantum non-locality.